nLab machine learning

Idea

Machine learning is a branch of computer science which devises algorithms to learn from data so as to perform tasks without being explicitly programmed to do so. Notable approaches include neural networks, support vector machines and Bayesian networks.

Related concepts

• neural network

• kernel method

• topological data analysis

• topological machine learning

• statistical learning theory

• singular learning theory

References

Classical machine learning

For a treatment in terms of category theory see

• Dan Shiebler, Bruno Gavranović, Paul Wilson, Category Theory in Machine Learning (arXiv:2106.07032)

See also:

• Wikipedia, Machine learning

With regards to kernel methods:

• Thomas Hofmann, Bernhard Schölkopf, Alexander J. Smola, Kernel methods in machine learning, Annals of Statistics 2008, Vol. 36, No. 3, 1171-1220 (arXiv:math/0701907)

• Julien Mairal, Jean-Philippe Vert, Machine Learning with Kernel Methods, 2017 (pdf, pdf)

Quantum machine learning

In view of quantum computation (ie. quantum machine learning):

• Diego Ristè, Marcus P. da Silva, Colm A. Ryan, Andrew W. Cross, Antonio D. Córcoles, John A. Smolin, Jay M. Gambetta, Jerry M. Chow & Blake R. Johnson,

  Demonstration of quantum advantage in machine learning, npj Quantum Information volume 3, Article number: 16 (2017) (doi:10.1038/s41534-017-0017-3)

• Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd, Quantum Machine Learning, Nature 549 (2017) 195–202 (doi:10.1038/nature23474)

  EurekaAlert, Quantum Machine Learning 14-Sep-2017

• Iris Cong, Soonwon Choi, Mikhail D. Lukin, Quantum convolutional neural networks, Nature Physics volume 15, pages 1273–1278 (2019) (doi:10.1038/s41567-019-0648-8)

  (on quantum neural networks)

• Yunchao Liu, Srinivasan Arunachalam, Kristan Temme, A rigorous and robust quantum speed-up in supervised machine learning (arXiv:2010.02174)

• Melanie Swan, Renato P dos Santos, Frank Witte, Between Science and Economics, Volume 2: Quantum Computing Physics, Blockchains, and Deep Learning Smart Networks, World Scientific 2020 (doi:10.1142/q0243)

• Stefano Mangini, Francesco Tacchino, Dario Gerace, Daniele Bajoni, Chiara Macchiavello, Quantum computing models for artificial neural networks, EPL (Europhysics Letters) 134(1), 10002 (2021) (arXiv:2102.03879)

and with emphasis on classically controlled NISQ-computes:

• John Preskill, Section 6.5 of: Quantum Computing in the NISQ era and beyond, Quantum 2018-08-06, volume 2, page 79 (arXiv:1801.00862, doi:10.22331/q-2018-08-06-79)

• Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, Keisuke Fujii, Quantum Circuit Learning, Phys. Rev. A 98, 032309 (2018) (arXiv:1803.00745)

• Marcello Benedetti, Erika Lloyd, Stefan Sack, Mattia Fiorentini, Parameterized quantum circuits as machine learning models, Quantum Science and Technology 4, 043001 (2019) (arXiv:1906.07682)

• Marco Radic, Quantum-enhanced Machine Learning in the NISQ era, 2019 (pdf, pdf)

• Dario Gerace, Quantum Machine Learning on NISQ hardware,, talk at INT online program on “Scientific Quantum Computing and Simulation on Near-Term Devices” 2020 (pdf, pdf)

• Andrea Mari, Thomas R. Bromley, Josh Izaac, Maria Schuld, Nathan Killoran, Transfer learning in hybrid classical-quantum neural networks, Quantum 4, 340 (2020) (arXiv:1912.08278)

• Lucas Munds, Quantum Machine Learning: A Roadmap for NISQ Era and Beyond, Oct 17, 2020

• Tirthajyoti Sarkar, TensorFlow Quantum: Marrying machine learning with quantum computing, Mar 11, 2020

• QunaSys, Tech Blog, Quantum machine learning of quantum data with NISQ devices (Feb 15 2021)

• TensorFlow.org (Google), Quantum Machine Learning

Applications

There are or will be innumerable applications. Here are some:

To mathematical structures in algebraic geometry, representation theory, number theory and combinatorics:

• Yang-Hui He, Machine-Learning Mathematical Structures, International Journal of Data Science in the Mathematical Sciences [arXiv:2101.06317, doi:10.1142/S2810939222500010]

reviewed in:

• Yang-Hui He, Machine-Learning Mathematical Structures, talk at M-Theory and Mathematics 2023, NYU Abu Dhabi (Jan 2023) [web]

To the conformal bootstrap:

• Gergely Kántor, Vasilis Niarchos, Constantinos Papageorgakis, Solving Conformal Field Theories with Artificial Intelligence (arXiv:2108.08859)

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